Simulation of magnetized ferric oxide nanoparticle flow over a stretching surface using a Levenberg–Marquardt backpropagation approach

The proposed study is to examine the application of blood flow in a 2D Non-Newtonian magnetic dipole over a stretching sheet incorporating ferrofluid nanoparticles. By employing appropriate similarity transformations, the system of PDEs is transformed into a set of coupled nonlinear ODEs. The result...

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Bibliographic Details
Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 47; no. 10; p. 464
Main Authors: Ahmed, Iftikhar, Azhar, Ehtsham, Ali, Hashmat, Jamal, Muhammad, Afaq, Harsa
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2025
Springer Nature B.V
Subjects:
Artificial neural networks
Back propagation networks
Blood flow
Boundary conditions
Charged particles
Engineering
Ferric oxide
Ferrofluids
Fluid flow
Graphical representations
Heat transfer
Investigations
Magnetic dipoles
Magnetic fields
Mechanical Engineering
Nanoparticles
Nusselt number
Ordinary differential equations
Partial differential equations
Radiation
Runge-Kutta method
Skin friction
Stretching
Technical Paper
Two dimensional flow
Velocity
Levenberg–Marquardt backpropagation method
Nanofluid
Magnetic dipole
Non-Newtonian fluid
Blood flow
ISSN:1678-5878, 1806-3691
Online Access:Get full text
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Summary:The proposed study is to examine the application of blood flow in a 2D Non-Newtonian magnetic dipole over a stretching sheet incorporating ferrofluid nanoparticles. By employing appropriate similarity transformations, the system of PDEs is transformed into a set of coupled nonlinear ODEs. The results were obtained using artificial neural networks (ANNs) in conjunction with the Levenberg–Marquardt backpropagation method (ANNs-LMBM). The Levenberg–Marquardt backpropagation method is a widely used optimization algorithm for training neural networks, specifically designed to effectively minimize the loss function that measures the difference between the neural network’s predicted output (based on a given input vector) and the true target output (the true value obtained from the numerical solution). Additionally, the Runge–Kutta shooting technique was employed to compare the results. Graphical representations were generated to illustrate the relevant parameters such as velocity, temperature, and concentration. Numerical outcomes for the local Nusselt number and local skin friction number were calculated under various parametric scenarios to reveal interesting features of the investigation. Replications using regression/correlation, state transitions, and error histograms were also discussed to validate the capability, validity, consistency, and accuracy of the ANNs-LMBM method.
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ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-025-05783-8